| 由扩张法构造带Novikov结构的李代数 |
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| 引用本文： | 胡建华,王资敏,曾博文.由扩张法构造带Novikov结构的李代数[J].上海理工大学学报,2017,39(5):416-419. |
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| 作者姓名： | 胡建华 王资敏 曾博文 |
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| 作者单位： | 上海理工大学 理学院, 上海 200093,上海理工大学 理学院, 上海 200093,上海理工大学 理学院, 上海 200093 |
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| 基金项目： | 上海理工大学教师教学发展研究基金资助项目（CFTD17015Z，CFTD17016Z） |
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| 摘 要： | 在特征为零的数域上给出构造李代数带Novikov结构的一种方法——扩张法.利用2-上循环和李代数表示,由一个阿贝尔李代数和一个任意李代数给出了扩张李代数的定义;带Novikov结构的李代数既具有仿射结构,也具有Novikov结构,恰当定义乘积后,给出了扩张李代数具有仿射结构的充要条件,给出了扩张李代数具有Novikov结构的充要条件.此方法在实际中仅适用于一些特殊的李代数,故给出了一个由扩张法构造带Novikov结构的低维李代数的实例.
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| 关 键 词： | 2-上循环 仿射结构 Novikov结构 扩张 |
| 收稿时间： | 2017/3/29 0:00:00 |
Construction of Lie Algebras with Novikov Structure via Extensions |
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| HU Jianhu,WANG Zimin and ZENG Bowen.Construction of Lie Algebras with Novikov Structure via Extensions[J].Journal of University of Shanghai For Science and Technology,2017,39(5):416-419. |
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| Authors: | HU Jianhu WANG Zimin and ZENG Bowen |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China,College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China and College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | A method via extension was proposed to construct Lie algebra with Novikov structure over a field of characteristic zero.Using 2-cocycle and the representations of Lie algebras,the definition of extended Lie algebras was given by an Abelian Lie algebra and an arbitrary Lie algebra.A Lie algebra with Novikov structure is endowed with both affine structure and Novikov structure.With a proper product defined,the necessary and sufficient conditions for the extended Lie algebras endowed with affine structure was given.And the necessary and sufficient conditions for the extended Lie algebras endowed with Novikov structure was given.In practice the method is only suited to some special Lie algebras.An example was presented of the low-dimensional Lie algebra with the Novikov structure constructed by extension. |
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| Keywords: | 2-cocycle affine structure Novikov structure extension |
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